Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Find the general indefinite integral.
$ \displaystyle \int 2^t (1 + 5^t)\, dt $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Gregory Higby
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:57
Frank Lin
00:50
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Missouri State University
Oregon State University
Idaho State University
Lectures
05:53
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
40:35
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
00:44
Find the indefinite integr…
00:37
Find the general indefinit…
00:35
Evaluate the indefinite in…
02:29
Find the integrals.$\i…
01:40
01:14
06:12
Evaluate the integral.
01:12
Find the integral.$\in…
01:19
right. The theme in this problem is that if you are asked to take a to the T. Power D. T. So the location of your expense important, uh The anti griddle is one divided by the natural log of T. Um times A. To the T. Power. And it's just undoing the chamber and you do need to remember plus your constant. So the key in this problem then is to get your problem to look like that uh to the T. One plus five to the T. Power DT. So what we need to do is because there's a multiplication right here, we need to distribute that in there before trying anything. And a rule here is that because we have to the T. Power. So there's T. Number of twos and there's T. Number of fives. That should be the same as two times 52 times five tee times. So it's the same thing as 10 to the T. Power. I hope my explanation made sense why that's true because now we can just use this rule up here. Uh put a boxer on that, that's what we're using. Um And it's going to be won over natural log of two times, two to the T. Power, plus one over natural log of 10 times 10 to the T. Power. And don't forget about plus C. You can verify that this is correct because the derivative of this will get us back to here, which we already know is equal to that, so we have the correct answer.
View More Answers From This Book
Find Another Textbook
00:47
Identify a rational number among the following numbers :2 + √2, 2√2, 0 a…
01:27
A is B's brother. c is A's mother. D is C's father. B is D…
02:38
77) A train passes a standing man in 15.3 sec andpasses a bridge of length 1…
In time wages system, wages are paid according to the _________ .
07:04
mohan lends out a sum to ramesh at 6% per annum si rate in such a way that r…
01:31
11. The sum of four consecutive natural numbers is 166. What are the numbers…
01:59
What least number should be subtracted from 11125 so that the resulting numb…
03:00
if a mixture contains 60% of milk anf the remaining is water. another contai…
02:52
If (-3, 0, 3) is a centroid of a triangle for which (3, -9, 11) , (-2, 5, 7…
05:47
. A dice is rolled. What is the chance thatthe upper face will be: (I) 3 (i…